Question

$y\mathrm{\alpha }\frac{1}{x^3}$ and x = 2 when y = 4 find y when x = 4.

Answer 1

$$\begin{gathered} Wehave: \\ y\alpha \frac{1}{x^3} \\ \Rightarrow y{x}^3=k\left(H\mathrm{ere},k\mathrm{is}\mathrm{constant}.\right) \\ \mathrm{Thus},wehave: \\ 4\times \left(2^3\right)=k\left(x=2\mathrm{when}y=4.\right) \\ \Rightarrow 4\times 8=k \\ \Rightarrow k=32 \\ \therefore y{x}^3=32\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \Rightarrow y{\left(4\right)}^3=32\left(\because x=4\right) \\ \Rightarrow y=\frac{32}{64}=\frac{1}{2} \end{gathered}$$